How can I get rid of an opossum that won’t leave my yard?

When frightened, opossums will sit there and hiss with their mouth open. If you find a possum that won't move, don't assume that it is injured. Most often, the opossum is frightened and will hold its ground and defend itself. Simply walk away and keep children and pets away. (Of course, you should make sure the opossum has not bitten any pet or person; if it has, contact your health department.) The opossum will move on when it feels safe.
Your yard may be the perfect habitat for an opossum. If so, you wouldn't expect it to leave and go to a site with poorer habitat. In this case, you must degrade the quality of the opossum habitat in your yard. Make sure there is no food available (trash, unpicked fruit or fruit on the ground, pet food, unprocessed compost). Make sure the opossum loses the habitat that protects it from the elements and predators (access to buildings or sheds, access to a hide-a-way in firewood or brush piles, untrimmed vegetation, under porches). In other words, make the best habitat for this opossum somewhere else, and not in your yard.
If the opossum is injured, contact local animal control, a wildlife rehabilitator, or a professional wildlife controller.
Resources: (online)
Opossum